REVISION

QUESTION 1 Suppose X is a random variable with the following distribution function. (a) Find (b) Find f(x)

SOLUTION (a) (b)

QUESTION 2 A random variable X is normally distributed with mean and standard deviation. Given that and . Find mean and standard deviation of the random variable X.

SOLUTION

QUESTION 3 On a certain day, a large number of fuses were manufactured. A sample of 80 fuses is drawn from the day’s production and 17 of them were found to be defective.   Find 95% confidence interval for the proportion of defective fuses manufactured that day. Find 99% confidence interval for the proportion of defective fuses manufactured that day. Compare the answer in (a) and (b). Explain the result. If the manufacture claims that the proportion of defective fuses manufactured that day is less than 30%. Perform a hypothesis test which can support the manufacture’s claim at . Does the manufacture’s claim true?

SOLUTION (a) (b)

(c)

QUESTION 4 A study is conducted to determine the difference of melting times of two types of chocolate; milk chocolate and white chocolate. A sample of eight people is selected to melt the milk chocolate and white chocolate. The melting times (in seconds) for every chocolate, are as follows: Test a hypothesis whether the mean melting time of milk chocolate differs with white chocolate by assume both population variances are equal. Use : (a) . (b) . (c) Is there any difference in conclusion in b (i) and (ii)? If yes, explain. Types of Chocolate   Melting Time Milk Chocolate 30 55 50 22 46 45 44 White Chocolate 58 23 64 105 93 28 80

SOLUTION (a)

(b) (c) Yes. As increases, the area of rejection also increase and tends to reject.

QUESTION 5 Inertial weight (in tons) and fuel economy (in mi/gal) were measured for a sample of seven diesel trucks. The results are presented in the following table. (a) Find the estimated regression line. (b) Calculate the correlation and interpret. (c) Test whether there is significant relationship between the inertial weight and fuel economy (mileage) at by using t-test. Weight (x) Mileage (y) 8.00 7.69 24.50 4.97 27.00 4.56 14.50 6.49 28.50 4.34 12.75 6.24 21.25 4.45

SOLUTION (a)

(b)

(c)

QUESTION 6 The sample data of heights for 12 fathers and their oldest son (in inches) were collected and the following statistical output was obtained. Write the simple linear regression model from the above output. Find the coefficient determination, , and interpret the result. Find the correlation, r, and interpret the result. Predict the height of son if the height of their father is 78 inches. Test the linear relationship between the height of son and the height of father at

SOLUTION (a) (b) (c) (d)

(e)

QUESTION 7 An industrial engineer at a furniture manufacturing plant wishes to investigate how the plant's electricity usage depends on the amount of the plant's production. He found that there is a simple linear relationship between production measured as the value in Ringgit Malaysia units of furniture produced in certain month (x) and the electrical usage in units of kWh (kilowatt-hours, y). 15 observations were collected and initial calculation needed in finding linear regression are shown below:

(a) Fit a simple linear regression model (a) Fit a simple linear regression model. (b) Test the linear relationship between x and y at α = 0.05 using t-test. What is the conclusion that can be made? (c) Calculate the value of coefficient of determination and interpret the result.

SOLUTION = 0.0125 = 1.0518 = 0.2638 = 0.0119 = 2.4299

(b) Since 0.0859 < 2.1604, we do not have enough evidence to conclude that there exist a linear relationship between the furniture production and electrical usage.

(c)